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Explore a comprehensive treatment of linear and quadratic quasinormal modes (QNMs and QQNMs) in second-order perturbation theory within Schwarzschild spacetime through this 26-minute conference lecture. Learn about novel methods for extracting QNM and QQNM amplitudes using Laplace transform treatment that accommodates arbitrary initial data. Discover how hyperboloidal foliation enables clean and efficient extraction of mode amplitudes at both future null infinity and the black-hole horizon. Examine the framework's impact on modeling complete second-order ringdown, essential for developing high-precision models of the black hole post-merger phase required for gravitational wave detection. Gain insights into advanced mathematical techniques that address non-linear effects in gravitational wave modeling, presented as part of the Workshop on Hyperboloidal Foliations and their Application at the Erwin Schrödinger International Institute for Mathematics and Physics.
